Computing the Maslov index from singularities of a matrix Riccati equation

Thomas McCauley

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arXiv · 1510.03736

Computing the Maslov index from singularities of a matrix Riccati equation

Thomas McCauley

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Abstract

We study the Maslov index as a tool to analyze stability of steady state solutions to a reaction-diffusion equation in one spatial dimension. We show that the path of unstable subspaces associated to this equation is governed by a matrix Riccati equation whose solution $S$ develops singularities when changes in the Maslov index occur. Our main result proves that at these singularities the change in Maslov index equals the number of eigenvalues of $S$ that increase to $+\infty$ minus the number of eigenvalues that decrease to $-\infty$.

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BibTeX RIS

Thomas McCauley. 2015-10-27. Computing the Maslov index from singularities of a matrix Riccati equation. https://arxiv.org/abs/1510.03736

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